Low Distortion Embedding of the Hamming Space into a Sphere with Quadrance Metric and k-means Clustering of Nominal-continuous Data

In this article we propose a new clustering algorithm for combinations of continuous and nominal data. The proposed algorithm is based on embedding of the nominal data into the unit sphere with a quadrance metrics, and adaptation of the general k-means clustering algorithm for the embedding data. It is also shown that the distortion of new embedding with respect to the Hamming metrics is less than that of other considered possibilities. A series of numerical experiments on real and synthetic datasets show that the proposed algorithm provide a comparable alternative to other clustering algorithms for combinations of continuous and nominal data.